請問:設f(x)具有f(x+1)-f(x)=5x-4之性質，則f(3)-f(1)之值為何？附上算式，感謝，急急急?

f(3) - f(1)
= f(3) - f(2) + f(2) - f(1)
= f(2+1)-f(2) + f(1+1)-f(1)
= 5(2)-4 + 5(1)-4
= 7

設f(x)=ax^2+bx+c
f(x+1)-f(x)
=a (x+1)^2 +b (x+1) + c - a x^2 - b x - c
=a (2x+1)+b
=5x-4

2a=5, a+b= - 4
a=5/2, b= -13/2

f(x)= (5/2)x^2 - (13/2)x + c ......Ans

f(3)-f(1)
=(5/2)(9-1)-(13/2)(3-1)
=20-13
=7 ....Ans